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Publications
Research published by Aletheia: browse the catalogue.
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Preprint · Version 1.0Preprint; not peer reviewed4 August 2026
Andrea Paone, Marco Paone
Adding an edge to a graph can push a quantity tied to its line graph past a threshold. The paper gives a condition that prevents that jump, and proves the condition survives two ways of growing the graph: splitting an edge into four, and attaching a module at any vertex. Starting from a pentagon, this builds an infinite family of graphs sitting exactly on the bound. The condition is enough, but it is not known to be necessary, and the general bound stays open.
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Preprint · Version 1.0Preprint; not peer reviewed1 August 2026
Andrea Paone, Marco Paone
For two families of graphs, roses and generalized theta graphs, the work computes in closed form how many eigenvalues of the line graph are positive, zero and negative. The result depends only on the lengths of the paths, counted modulo four.
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Preprint · Version 2.0-rev2Preprint; not peer reviewed1 August 2026
Andrea Paone
Research seriesVersion 2.0-rev2 · current revision of Version 2
Not one isolated counterexample but an infinite family, inside a class of very simple graphs, with the means to carry the result from one graph to another and exact certificates for every case.
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PreprintPreprint; not peer reviewed30 July 2026
Andrea Paone, Marco Paone
An upper bound that holds for every graph, constructions that reach it, and counterexamples to a simplification that looked natural. Every case is checked with exact arithmetic, not approximation.
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Preprint · Version 1Preprint; not peer reviewed22 July 2026
Andrea Paone
Research seriesVersion 1 · historical finite-counterexample record
A finite connected simple counterexample to Conjecture 4.12 on line-graph inertia indices, accompanied by exact certificates.
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Research area
Digital security, critical-infrastructure resilience, and responsible governance of artificial intelligence systems.
Research reportIndependent research report; not peer reviewed18 July 2026
Andrea Paone
A source-audited assessment of whether the EU's 2026 Action Plan turns cyber and AI regulation into operational capability for critical infrastructure.
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